Problem: Solve for $x$ : $4x^2 + 40x + 84 = 0$
Explanation: Dividing both sides by $4$ gives: $ x^2 + {10}x + {21} = 0 $ The coefficient on the $x$ term is $10$ and the constant term is $21$ , so we need to find two numbers that add up to $10$ and multiply to $21$ The two numbers $3$ and $7$ satisfy both conditions: $ {3} + {7} = {10} $ $ {3} \times {7} = {21} $ $(x + {3}) (x + {7}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 3) (x + 7) = 0$ $x + 3 = 0$ or $x + 7 = 0$ Thus, $x = -3$ and $x = -7$ are the solutions.